term

class liesel_ptm.term(basis, penalty, scale, name, inference=None, coef_name=None, _update_on_init=True)

Bases: UserVar

General structured additive term.

A structured additive term represents a smooth or structured effect in a generalized additive model. The term wraps a design/basis matrix together with a prior/penalty and a set of coefficients. The object exposes the coefficient variable and evaluates the term as the matrix-vector product of the basis and the coefficients. The term evaluates to basis @ coef.

Parameters:

• basis (Basis) – A Basis instance that produces the design matrix for the term. The basis must evaluate to a 2-D array with shape (n_obs, n_bases).

• penalty (Var | Value | Any) – Penalty matrix or a variable/value wrapping the penalty used to construct the multivariate normal prior for the coefficients.

• scale (Var | Any) – Scale parameter for the prior on the coefficients. This is typically either a scalar or a per-coefficient scale variable.

• name (str) – Human-readable name for the term. Used for labelling variables and building sensible default names for internal nodes.

• inference (Any) – liesel.goose.MCMCSpec inference specification forwarded to coefficient creation. (default: None)

• coef_name (str | None) – Name for the coefficient variable. If None, a default name based on name will be used. (default: None)

• _update_on_init (bool) – If True (default) the internal calculation/graph nodes are evaluated during initialization. Set to False to delay initial evaluation. (default: True)

Raises:

ValueError – If basis.value does not have two dimensions.

scale

The scale variable used by the prior on the coefficients.

nbases

Number of basis functions (number of columns in the basis matrix).

basis

The basis object provided to the constructor.

coef

The coefficient variable created for this term. It holds the prior (multivariate normal singular) and is used in the evaluation of the term.

is_noncentered

Whether the term has been reparameterized to the non-centered form.

Examples

Create a P-spline basis and wrap it into a term:

# assume x to be a 1d array.
b = ps(x, nbases=10)
t = term(basis=b, penalty=b.penalty, name="f(x)")

Methods

f	Construct a smooth term from a Basis.
f_ig	Construct a smooth term with an inverse-gamma prior on the variance.
reparam_noncentered	Turns this term into noncentered form, which means the prior for the coefficient will be turned from coef ~ N(0, scale^2 * inv(penalty)) into latent_coef ~ N(0, inv(penalty)); coef = scale * latent_coef.

Attributes

includes_intercept